Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
704 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#16862234 | C2 | semidirect |
| 3. C2×#16862234 | C2 | semidirect |
| 4. C2×C4×D524 | C2 | semidirect |
| 5. #22553229 | C2 | semidirect |
| 6. #22553218 | C2 | semidirect |
| 7. #22553214 | C2 | semidirect |
| 8. #22553190 | C2 | semidirect |
| 9. C4×C4⋊C4×C131 | C2 | semidirect |
| 63. C42×C131 | D4 | semidirect |
| 127. C131 | #2544 | semidirect |
| 137. C4×C4⋊C4 | D131 | semidirect |
| 191. C42 | D524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862243 | 2 |
| C2×#16862234 | 2 |
| C2×C4×D524 | 2 |
| #22553229 | 2 |
| #22553218 | 2 |
| #22553214 | 2 |
| #22553190 | 2 |
| C4×C4⋊C4×C131 | 2 |
| #2544 | 131 |